Well past midnightCalling time on implicit invariant learning

Ben R Newell and James EH BrightUniversity of New South Wales Sydney Australia

Three experiments are reported that examine the nature of knowledge under-lying performance in the invariant learning task Previous research (Bright ampBurton 1994 McGeorge amp Burton 1990) has supported an account of perfor-mance based on the implicit abstraction and application of a rule pertaining tothe invariant feature In contrast we found effects in both the digit and clockinvariant tasks that are difficult to explain solely in terms of subjects acquiringthe experimentersrsquo rule In all three experiments manipulation of test itemproperties that are independent of the invariant feature led to a detriment in per-formance that is not predicted by an account based on the experimentersrsquo rulesFurthermore the use of an on-line measure of awareness (confidence ratings)provided some evidence that performance is mediated by low confidence expli-cit knowledge

Early accounts of implicit learningmdasha process of unintentionally acquiring asensitivity to a set of stimulimdashposited a powerful unconscious mechanismcapable of abstracting rules that describe the underlying structure of a stimulusenvironment (eg Reber 1967 1976) Under such an account performanceimprovements are attributable to the application of the acquired rules to novelstimuli Subsequent accounts (eg Brooks 1978 Perruchet amp Gallego 1997)state that implicit learning is not characterised by rule acquisition but rather bythe storage of discrete instances in memory According to this view improve-ments in performance result from a similarity-match between novel stimuli andstored instances or fragments thereof (eg Perruchet amp Pacteau 1990) ofpreviously encountered stimuli

EUROPEAN JOURNAL OF COGNITIVE PSYCHOLOGY 2002 14 (2) 185ndash205

Requests for reprints should be addressed to B Newell Department of Psychology UniversityCollege London Gower Street London WC1E 6BT UK Email bnewelluclacuk

Ben Newell was supported by a Commonwealth Scholarship Jim Bright was supported by anAustralian Research Council Small Grant We would like to thank Peter Lovibond Fred WestbrookAxel Cleeremans Pierre Perruchet and one anonymous reviewer for their helpful comments on anearlier draft of this paper We also thank Sally Andrews for assisting in collecting the data forExperiment 2

2002 Psychology Press Ltdhttpwwwtandfcoukjournalspp09541446html DOI10108009541440143000023

The relative merits of these two accounts have been extensively researchedover the last 20 years and it has become clear that an explanation of implicitlearning based solely on implicit rule abstraction has become increasingly dif-ficult to justify (Gomez 1997 Gomez amp Schvaneveldt 1994 Shanks ampJohnstone 1998 Vokey amp Brooks 1992)

One paradigm that reflects this on-going debate is the invariant learning tasksof Burton and colleagues (Bright amp Burton 1994 Cock Berry amp Gaffan 1994McGeorge amp Burton 1990 Wright amp Burton 1995) In one version of thisparadigm (the Bright and Burton clocks task) the case for an implicit rule-basedaccount is still strongly argued (Bright amp Burton 1994 1998) whereas in otherversions (the McGeorge amp Burton 3s task 1990) existing studies leave open thepossibility of similarity-based processing (Cock et al 1994 Wright amp Burton1995)

In the experiments presented here we examine two demonstrations ofinvariant learning in an attempt to determine the nature of the representationsunderlying subjectsrsquo performance In particular we aim to assess the capabilityof an implicit rule-based account to explain the learning effects observed in theinvariant paradigm

Implicit invariant learning is said to have occurred when a person demon-strates an acquired sensitivity to an invariant characteristic of a set of stimuli inthe absence of verbal knowledge of that characteristic In the original demon-stration McGeorge and Burton (1990) showed subjects 30 four-digit numberstrings in an incidental learning task All the strings presented to the subjectscontained the digit 3 though this invariant feature was not brought to theattention of the subjects In a subsequent surprise test phase subjects wereshown 10 pairs of novel four-digit strings where one string in each pair con-tained a 3 (the positive) and the other did not (the negative) Subjects were told(falsely) that they had seen one and only one of the strings in the previouslearning phase and were instructed to choose the one they thought they had seenbefore The reliable finding was that subjects chose more positives than wouldbe expected by chance (typically 6 or 7 out of 10) This preference persistedwhen the surface representation of strings was changed from numeric (3457)during learning to word (three five two one) at test

Bright and Burton (1994) extended the original finding to the learning of amore complex invariant feature Bright and Burton showed subjects 30schematic clock faces that all depicted times between 6 and 12 orsquoclock Thusthe position of the hour hand was the invariant feature At test subjects wereshown 10 novel pairs of clocks with one showing a time inside the invariantrange (positive) and one 6 hours away from that time (negative) (eg 830 and230) Once again the robust finding was that subjects showed a selectionpreference for the positives A change in surface representation from analogueduring learning to digital at test had no effect on subjectsrsquo preferences

186 NEWELL AND BRIGHT

The surprising finding in both these demonstrations was that subjects per-formed above chance at test in spite of being unable to verbalise any knowledgepertaining to the invariant feature Indeed many subjects expressed surprisewhen told about the nature of the underlying invariant rule

McGeorge and Burton (1990) and Bright and Burton (1994 1998) argued thatthe simplest explanation of these findings was that subjects were implicitlylearning the critical invariant rule

However as a number of investigators have pointed out (Berry amp Cock1998 Churchill amp Gilmore 1998 Cock et al 1994 Wright amp Burton 1995Wright amp Whittlesea 1998) rather than responding on the basis of the infor-mation that the experimenter assumes the subject has acquired the subject maybe utilising other correlated information to make selections based on the simi-larity (Cock et al 1994) or unfamiliarity (Churchill amp Gilmore 1998 Wright ampBurton 1995) of test items in comparison with learning items

Wright and Burton (1995) suggested that the correlated information used bysubjects in the lsquolsquo3srsquorsquo task was the presence of distinctive featuresmdashrepetitionsmdashin the strings An analysis of the typical learning strings used in the McGeorgeand Burton experiment showed that constraining all strings to contain a lsquolsquo3rsquorsquoreduced the probability of repeated digits (eg 5772 or 7572) occurring Theynoted that the probability of repeated digits appearing in a positive (stringcontaining the invariant 3) was 034 compared to the probability of 059 ofrepeated digits appearing in a negative (string without a 3) Wright and Burtonrsquoshypothesis was that subjects score at an above-chance level not because thepositives conform to an implicitly learnt rule but because it is easy to rejectdistinctive items (ie those with repetitions) seen at test Their results indicatedthat 64 of test decisions could be classified as involving rejection of thedistinctive item compared with 59 of occasions in which the positive wasselected Wright and Burton concluded that subjectsrsquo behaviour was betterclassified as lsquolsquorejecting repetitionsrsquorsquo than lsquolsquoaccepting positivesrsquorsquo (1995 p 794)

This explanation of subjectsrsquo behaviour accounts well for the simple versionof the invariant 3 taskmdashthat is when both learning and test items are representedin the same surface format (ie digits) However in the original demonstrationMcGeorge and Burton (1990) showed that subjectsrsquo preferences for itemscontaining the 3 persisted when the surface representation was changed fromdigits at learning to words at test To date the rejection strategy of Wright andBurton (1995) has not been tested to see if it can account for subjectsrsquo behaviourin this cross-format transfer condition It is possible that the effects observed byWright and Burton (1995) were based on perceptual recognition where there isan advantage for items that bear the same perceptual characteristics during boththe learning and test phases The importance of perceptual characteristics hasbeen demonstrated in the implicit memory literature where a number of studieshave shown that a change in surface representation between learning and test

INVARIANT LEARNING 187

results in reduced priming effects (eg Blaxton 1989 Jacoby amp Hayman1987)

In Experiment 1 we test the rejection strategy of Wright and Burton (1995)and examine whether subjectsrsquo tendency to reject items containing repeateddigits interacts with a change in the perceptual format of items between thelearning and test phase If an interaction were obtained this would suggest thatthe rejection strategy proposed by Wright and Burton is not a genericmechanism underlying performance in the invariant 3s task An interactionwould suggest that the tendency to reject distinctive items is observed only whenthe perceptual format of learning and test items is the same In contrast thefailure to find an interaction would demonstrate that the rejection strategyoperates under both same and cross-format transfer conditions

EXPERIMENT 1

Method

Participants Thirty undergraduate students from the University of NewSouth Wales participated in the experiment in return for course credit All wereaged between 18 and 30 years All were na otilde Egrave ve with respect to the invariantlearning procedure

Materials Learning sets were generated by selecting randomly 30 numberstrings from a database containing all 2048 possible four-digit numbersconstructed from the digits 1 to 9 and containing a single digit 3 Test setswere generated from four databases one containing all possible four digitnumbers with a single lsquolsquo3rsquorsquo and with no repetitions one with a single lsquolsquo3rsquorsquo andwith repetitions one with no lsquolsquo3rsquorsquo and no repetitions and one with no lsquolsquo3rsquorsquo andwith repetitions Following Wright and Burton (1995) quadruples triples anddouble doubles were removed from the databases leaving only doubles to serveas distinctive items Items containing a 3 were termed positives and thosewithout a 3 negatives Test sets contained three types of pairs those biasingsubjects towards positive selection those biasing subjects against positiveselection and those that were neutral with respect to positive selection That is

(1) the negative contained a double but positive did notmdashthis should biassubjects towards selection of the positive (eg 5772 vs 2367)

(2) the positive contained a double but negative did notmdashthis should biassubjects against selection of the positive (eg 3525 vs 2167)

(3) that neither the positive nor the negative contained a doublemdashthis shouldbe neutral with respect to selection of the positive (eg 3428 vs 7865)

Each subject received twelve pairs four from each of the three pair types Alllearning items were printed in numeric format (1357) test items were printed ineither numeric or word format (one three five seven)

188 NEWELL AND BRIGHT

Design and procedure A mixed design was used The within-subjectsfactor was direction of bias this had three levels towards neutral against Thebetween-subjects factor was test format with two levels same or changedSubjects were randomly assigned to one of the two groups The lsquolsquosamersquorsquo grouplearned and were tested on numeric items the lsquolsquochangedrsquorsquo group learned onnumeric items and were tested on word items The dependent variable was thenumber of positives selected at test

The experiment consisted of three phases learning an unexpected test andpost-test questioning Subjects were shown 30 four-digit numbers containingthe digit 3 and were asked to perform an addition and comparison task oneach number This involved adding together the first two digits and compar-ing the sum with the total of the second two digits After completing thistask learning materials were removed from sight and subjects were presentedwith 12 test pairs in numeric (same group) or word (changed group) formatand were told (falsely) that they had seen one item in each pair before Theleftright position of the positive and negative and the order of presentation ofthe three pair types were counterbalanced Subjects were asked to indicatewhich item they thought they had seen before and to guess if they wereunsure On completion of the test phase a questionnaire was presented to thesubjects (see the Appendix) On completion of the questionnaire subjectswere fully debriefed

Results

The mean number of positives selected was 613 (out of a maximum of 12) SD= 15 A single sample t-test showed that this was not significantly different fromchance performance of 6 [t(29) = 050 p gt 1] A 2 (Test Format samechanged) 6 3 (Direction of Bias towards neutral against) mixed modelanalysis of variance was conducted This revealed a significant main effect ofdirection of bias [F(2 56) = 462 p lt 05] and no significant effect of testformat [F(1 28) = 185 p gt 05] The interaction between test format anddirection of bias was not significant [F(2 56) = 113 p gt 05] The meannumbers of positives selected in each cell of the 2 6 3 design are presented inTable 1

TABLE 1Mean selection of positives (out of four) and standard

deviations by condition (Experiment 1)

Test format Towards Neutral Against

Same (digit) 273 (122) 193 (110) 207 (110)Changed (word) 253 (119) 213 (099) 133 (097)

INVARIANT LEARNING 189

In order to be confident that subjectsrsquo tendency to reject items containingrepeated digits extended to the changed format condition we conducted a one-way (direction of bias) repeated measures ANOVA on the data from this con-dition A significant main effect [F(2 28) = 442 p lt 05] was founddemonstrating that subjects do tend to reject distinctive items when the per-ceptual format is changed between learning and test phases Planned contrastsconducted on combined data from the same and changed format conditionsshowed a significant difference between the towards and against condition[F(1 28) = 918 MSe = 142 p lt 05 (Fc = 648)] Contrasts between towardsand neutral and against and neutral were not significant Mean selection scoreswere then compared against chance performance (2 for each condition) For thetowards condition more positives were selected than would be expected bychance [t(29) = 292 p lt 01] for the neutral and against conditions selectionwas at chance [t(29) = 18 p gt 1 t(29) = 151 p gt 1 respectively]

Following Wright and Burton (1995) the mean selection scores in eachcondition were converted to percentages to determine the proportion ofresponses that could be classified as involving rejections In the towards con-dition items containing doubles were rejected on 65 of occasions In theagainst condition 42 of items containing doubles were selected leaving 58rejected This means that over these two conditions 61 of decisions wereclassified as involving rejection of items containing repeated numbers Thiscompares to the 54 of decisions involving selection of the items containing theinvariant 3

Test of explicit knowledge All subjects (N = 30) reported that some of theirresponses at test were guesses When questioned about the strategy theyemployed when guessing seven could provide no justification for their guessesand a further thirteen mentioned memory or familiarity without elaborating onthe way in which it was used However four subjects reported relatively detailedstrategies including rejecting items with totals that equalled each otherchoosing items with totals closer together (eg 7673 over 2198) and choosingthe item in which the left pair total was larger than the right pair due to aperceived preponderance of these items in the learning set Analysis of thelearning and test sets used by these subjects revealed that performance predictedby the use of these strategies approximately matched actual performance in allcases This finding indicates that these subjects were using explicit veridicalknowledge and not merely providing post hoc explanations of their behaviour Afurther six subjects mentioned grounding their responses on double digits (bydouble they referred only to contiguous doubles eg 77 or seven seven) Thesesubjectsrsquo responses were further analysed to see if they conformed to theirexplicit knowledge We found that when the contiguous double was in thenegative item (towards condition) positives were selected on 83 of occasionsin comparison when the contiguous double was in the positive item (against

190 NEWELL AND BRIGHT

condition) selection of the positive was at 33 This suggests that these subjectswere responding to some extent on the basis of the presence or absence ofdouble digits In terms of positive selection these subjects did not appear toperform any better than subjects who did not rely on explicit knowledge ofdouble digits 66 (SD 149) compared to 55 (SD 164) Neither groupperformed significantly differently from chance (ps gt 1)

Finally explicit knowledge of the invariant 3 was examined When asked tocircle the number that they thought had appeared most frequently in the learningitems eight subjects circled the number 3 This is more than the 33 subjectspredicted by chance The mean positive selection for these subjects was 60(chance performance) and marginally lower than the mean for the whole group(613) This finding suggests that knowledge of the 3 was not used in the testphase but may have been cued by the questionnaire Many subjects expressedsurprise when told about the nature of the experiment during debriefing

Discussion

Experiment 1 has demonstrated that subjectsrsquo tendency to reject items con-taining repeated digits does not interact with a change in the perceptual formatbetween learning and test items Prior to Experiment 1 the rejection strategy hadnot been tested in cross-format transfer conditions leaving open the possibilitythat the effects observed by Wright and Burton were due to perceptual-basedrecognition We can now be confident that the rejection strategy can account forboth same-format and cross-format versions of the invariant digit task

Experiment 1 has provided further stronger evidence that subjects in theinvariant digit task do not learn the rule that it was originally supposed subjectslearnt in this task (ie lsquolsquoSelect items containing a 3rsquorsquo) The question of whatknowledge subjects are acquiring remains open to debate It is possible thatsubjects are applying an explicit (for some subjects at least) lsquolsquoreject repetitionsrsquorsquorule or that the rejection is part of a more general similarity-based mechanism inwhich test strings are compared (implicitly or explicitly) with memories oflearning strings We will return to this debate in the General Discussion andquestion whether it is possible (within the invariant task) to distinguish betweenrule- and similarity-based behaviour

Our finding of further evidence that subjects are not learning the experi-mentersrsquo rules in the 3s task leads us to question whether performance in thelogically related clocks task (Bright amp Burton 1994 1998) is based solely on theexperimentersrsquo rule pertaining to the invariant time range It is possible that theuse of information correlated with the rule that we and others (eg Cock et al1994 Wright amp Burton 1995) have observed in the digit task may be due to thenature of the numeric stimuli used It is plausible that certain structural char-acteristics of the number strings lend themselves to this type of processing Aclearer indication of a generic mechanism underlying invariant learning would

INVARIANT LEARNING 191

come from finding that the observed effects generalise to the more complexclock stimuli of Bright and Burton (1994 1998)

EXPERIMENT 2

A logical way to look for similar effects would be to test for a rejection strategyusing the clock stimuli However the nature of the stimuli make it extremelydifficult to design a lsquolsquorejectionrsquorsquo test set In our minds there seems to be nocorrelated feature (such as repetitions) that varies with the invariant time rangeLikewise manipulation of the specific similarity of learning and test items is alsoproblematic due to the way in which the clock stimuli are constructed For thisreason we manipulated other properties of the test pairs that we hypothesisedwould have an effect on subjectsrsquo decisions at test Bright and Burton (19941998) argued that performance in the clock task was indicative of implicit ruleabstraction If subjects are abstracting a rule during learning then presumably itwould be of the form lsquolsquofavour times between 6 and 12rsquorsquo (Bright amp Burton 1994p 81) If we accept this then provided one time in each pair is between 6 and 12and the other time is outside this range we would expect to observe the normalselection preference Alternatively subjects may be engaging in a comparisonprocess similar to the one that may underlie the rejection strategy If subjects aremaking comparisons of test items with learning items then reducing the similaritybetween learning and test items should be detrimental to performance InExperiment 2 we contrast performance on test pairs with differing degrees ofintra-test pair similarity Test pairs with a low similarity between times (thoseseparated by 6 hours eg 830 vs 230) are compared with pairs with a mediumsimilarity (those separated by 3 hours eg 430 vs 730) and with pairs with ahigh similarity (those separated by 1 hour eg 510 vs 610) If performance isbased on the lsquolsquo6 to 12rsquorsquo rule we expect no differences between the pair typesHowever if subjects are engaged in similarity-based processing we expectselection of the invariant in the 1-hour pairs to be lower than in the 6-hour pairs

Any observed differences between the pair types could be due to subjectsbeing biased into making comparisons by the nature of the pre-test instructionCock et al (1994) raised the possibility that the instruction to rely on memorycues subjects to engage in a post hoc comparison To test this claim they con-ducted a standard 3s task but replaced the memory instruction with a lsquolsquorulersquorsquoinstruction (Cock et al 1994 Experiment 3) Prior to the test phase of theexperiment subjects were informed that all learning items conformed to asimple rule and that test items conforming to this rule should be selectedPatterns of performance were similar to those of normal lsquolsquomemoryrsquorsquo instructionsubjects In Experiment 2 we control for the possibility of instructional bias onpair type selection We directly compare the performance of a group given thestandard memory instruction at test with one given an instruction to classifyitems on the basis of a rule

192 NEWELL AND BRIGHT

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

The surprising finding in both these demonstrations was that subjects per-formed above chance at test in spite of being unable to verbalise any knowledgepertaining to the invariant feature Indeed many subjects expressed surprisewhen told about the nature of the underlying invariant rule

McGeorge and Burton (1990) and Bright and Burton (1994 1998) argued thatthe simplest explanation of these findings was that subjects were implicitlylearning the critical invariant rule

However as a number of investigators have pointed out (Berry amp Cock1998 Churchill amp Gilmore 1998 Cock et al 1994 Wright amp Burton 1995Wright amp Whittlesea 1998) rather than responding on the basis of the infor-mation that the experimenter assumes the subject has acquired the subject maybe utilising other correlated information to make selections based on the simi-larity (Cock et al 1994) or unfamiliarity (Churchill amp Gilmore 1998 Wright ampBurton 1995) of test items in comparison with learning items

Wright and Burton (1995) suggested that the correlated information used bysubjects in the lsquolsquo3srsquorsquo task was the presence of distinctive featuresmdashrepetitionsmdashin the strings An analysis of the typical learning strings used in the McGeorgeand Burton experiment showed that constraining all strings to contain a lsquolsquo3rsquorsquoreduced the probability of repeated digits (eg 5772 or 7572) occurring Theynoted that the probability of repeated digits appearing in a positive (stringcontaining the invariant 3) was 034 compared to the probability of 059 ofrepeated digits appearing in a negative (string without a 3) Wright and Burtonrsquoshypothesis was that subjects score at an above-chance level not because thepositives conform to an implicitly learnt rule but because it is easy to rejectdistinctive items (ie those with repetitions) seen at test Their results indicatedthat 64 of test decisions could be classified as involving rejection of thedistinctive item compared with 59 of occasions in which the positive wasselected Wright and Burton concluded that subjectsrsquo behaviour was betterclassified as lsquolsquorejecting repetitionsrsquorsquo than lsquolsquoaccepting positivesrsquorsquo (1995 p 794)

This explanation of subjectsrsquo behaviour accounts well for the simple versionof the invariant 3 taskmdashthat is when both learning and test items are representedin the same surface format (ie digits) However in the original demonstrationMcGeorge and Burton (1990) showed that subjectsrsquo preferences for itemscontaining the 3 persisted when the surface representation was changed fromdigits at learning to words at test To date the rejection strategy of Wright andBurton (1995) has not been tested to see if it can account for subjectsrsquo behaviourin this cross-format transfer condition It is possible that the effects observed byWright and Burton (1995) were based on perceptual recognition where there isan advantage for items that bear the same perceptual characteristics during boththe learning and test phases The importance of perceptual characteristics hasbeen demonstrated in the implicit memory literature where a number of studieshave shown that a change in surface representation between learning and test

INVARIANT LEARNING 187

results in reduced priming effects (eg Blaxton 1989 Jacoby amp Hayman1987)

In Experiment 1 we test the rejection strategy of Wright and Burton (1995)and examine whether subjectsrsquo tendency to reject items containing repeateddigits interacts with a change in the perceptual format of items between thelearning and test phase If an interaction were obtained this would suggest thatthe rejection strategy proposed by Wright and Burton is not a genericmechanism underlying performance in the invariant 3s task An interactionwould suggest that the tendency to reject distinctive items is observed only whenthe perceptual format of learning and test items is the same In contrast thefailure to find an interaction would demonstrate that the rejection strategyoperates under both same and cross-format transfer conditions

EXPERIMENT 1

Method

Participants Thirty undergraduate students from the University of NewSouth Wales participated in the experiment in return for course credit All wereaged between 18 and 30 years All were na otilde Egrave ve with respect to the invariantlearning procedure

Materials Learning sets were generated by selecting randomly 30 numberstrings from a database containing all 2048 possible four-digit numbersconstructed from the digits 1 to 9 and containing a single digit 3 Test setswere generated from four databases one containing all possible four digitnumbers with a single lsquolsquo3rsquorsquo and with no repetitions one with a single lsquolsquo3rsquorsquo andwith repetitions one with no lsquolsquo3rsquorsquo and no repetitions and one with no lsquolsquo3rsquorsquo andwith repetitions Following Wright and Burton (1995) quadruples triples anddouble doubles were removed from the databases leaving only doubles to serveas distinctive items Items containing a 3 were termed positives and thosewithout a 3 negatives Test sets contained three types of pairs those biasingsubjects towards positive selection those biasing subjects against positiveselection and those that were neutral with respect to positive selection That is

(1) the negative contained a double but positive did notmdashthis should biassubjects towards selection of the positive (eg 5772 vs 2367)

(2) the positive contained a double but negative did notmdashthis should biassubjects against selection of the positive (eg 3525 vs 2167)

(3) that neither the positive nor the negative contained a doublemdashthis shouldbe neutral with respect to selection of the positive (eg 3428 vs 7865)

Each subject received twelve pairs four from each of the three pair types Alllearning items were printed in numeric format (1357) test items were printed ineither numeric or word format (one three five seven)

188 NEWELL AND BRIGHT

Design and procedure A mixed design was used The within-subjectsfactor was direction of bias this had three levels towards neutral against Thebetween-subjects factor was test format with two levels same or changedSubjects were randomly assigned to one of the two groups The lsquolsquosamersquorsquo grouplearned and were tested on numeric items the lsquolsquochangedrsquorsquo group learned onnumeric items and were tested on word items The dependent variable was thenumber of positives selected at test

The experiment consisted of three phases learning an unexpected test andpost-test questioning Subjects were shown 30 four-digit numbers containingthe digit 3 and were asked to perform an addition and comparison task oneach number This involved adding together the first two digits and compar-ing the sum with the total of the second two digits After completing thistask learning materials were removed from sight and subjects were presentedwith 12 test pairs in numeric (same group) or word (changed group) formatand were told (falsely) that they had seen one item in each pair before Theleftright position of the positive and negative and the order of presentation ofthe three pair types were counterbalanced Subjects were asked to indicatewhich item they thought they had seen before and to guess if they wereunsure On completion of the test phase a questionnaire was presented to thesubjects (see the Appendix) On completion of the questionnaire subjectswere fully debriefed

Results

The mean number of positives selected was 613 (out of a maximum of 12) SD= 15 A single sample t-test showed that this was not significantly different fromchance performance of 6 [t(29) = 050 p gt 1] A 2 (Test Format samechanged) 6 3 (Direction of Bias towards neutral against) mixed modelanalysis of variance was conducted This revealed a significant main effect ofdirection of bias [F(2 56) = 462 p lt 05] and no significant effect of testformat [F(1 28) = 185 p gt 05] The interaction between test format anddirection of bias was not significant [F(2 56) = 113 p gt 05] The meannumbers of positives selected in each cell of the 2 6 3 design are presented inTable 1

TABLE 1Mean selection of positives (out of four) and standard

deviations by condition (Experiment 1)

Test format Towards Neutral Against

Same (digit) 273 (122) 193 (110) 207 (110)Changed (word) 253 (119) 213 (099) 133 (097)

INVARIANT LEARNING 189

In order to be confident that subjectsrsquo tendency to reject items containingrepeated digits extended to the changed format condition we conducted a one-way (direction of bias) repeated measures ANOVA on the data from this con-dition A significant main effect [F(2 28) = 442 p lt 05] was founddemonstrating that subjects do tend to reject distinctive items when the per-ceptual format is changed between learning and test phases Planned contrastsconducted on combined data from the same and changed format conditionsshowed a significant difference between the towards and against condition[F(1 28) = 918 MSe = 142 p lt 05 (Fc = 648)] Contrasts between towardsand neutral and against and neutral were not significant Mean selection scoreswere then compared against chance performance (2 for each condition) For thetowards condition more positives were selected than would be expected bychance [t(29) = 292 p lt 01] for the neutral and against conditions selectionwas at chance [t(29) = 18 p gt 1 t(29) = 151 p gt 1 respectively]

Following Wright and Burton (1995) the mean selection scores in eachcondition were converted to percentages to determine the proportion ofresponses that could be classified as involving rejections In the towards con-dition items containing doubles were rejected on 65 of occasions In theagainst condition 42 of items containing doubles were selected leaving 58rejected This means that over these two conditions 61 of decisions wereclassified as involving rejection of items containing repeated numbers Thiscompares to the 54 of decisions involving selection of the items containing theinvariant 3

Test of explicit knowledge All subjects (N = 30) reported that some of theirresponses at test were guesses When questioned about the strategy theyemployed when guessing seven could provide no justification for their guessesand a further thirteen mentioned memory or familiarity without elaborating onthe way in which it was used However four subjects reported relatively detailedstrategies including rejecting items with totals that equalled each otherchoosing items with totals closer together (eg 7673 over 2198) and choosingthe item in which the left pair total was larger than the right pair due to aperceived preponderance of these items in the learning set Analysis of thelearning and test sets used by these subjects revealed that performance predictedby the use of these strategies approximately matched actual performance in allcases This finding indicates that these subjects were using explicit veridicalknowledge and not merely providing post hoc explanations of their behaviour Afurther six subjects mentioned grounding their responses on double digits (bydouble they referred only to contiguous doubles eg 77 or seven seven) Thesesubjectsrsquo responses were further analysed to see if they conformed to theirexplicit knowledge We found that when the contiguous double was in thenegative item (towards condition) positives were selected on 83 of occasionsin comparison when the contiguous double was in the positive item (against

190 NEWELL AND BRIGHT

condition) selection of the positive was at 33 This suggests that these subjectswere responding to some extent on the basis of the presence or absence ofdouble digits In terms of positive selection these subjects did not appear toperform any better than subjects who did not rely on explicit knowledge ofdouble digits 66 (SD 149) compared to 55 (SD 164) Neither groupperformed significantly differently from chance (ps gt 1)

Finally explicit knowledge of the invariant 3 was examined When asked tocircle the number that they thought had appeared most frequently in the learningitems eight subjects circled the number 3 This is more than the 33 subjectspredicted by chance The mean positive selection for these subjects was 60(chance performance) and marginally lower than the mean for the whole group(613) This finding suggests that knowledge of the 3 was not used in the testphase but may have been cued by the questionnaire Many subjects expressedsurprise when told about the nature of the experiment during debriefing

Discussion

Experiment 1 has demonstrated that subjectsrsquo tendency to reject items con-taining repeated digits does not interact with a change in the perceptual formatbetween learning and test items Prior to Experiment 1 the rejection strategy hadnot been tested in cross-format transfer conditions leaving open the possibilitythat the effects observed by Wright and Burton were due to perceptual-basedrecognition We can now be confident that the rejection strategy can account forboth same-format and cross-format versions of the invariant digit task

Experiment 1 has provided further stronger evidence that subjects in theinvariant digit task do not learn the rule that it was originally supposed subjectslearnt in this task (ie lsquolsquoSelect items containing a 3rsquorsquo) The question of whatknowledge subjects are acquiring remains open to debate It is possible thatsubjects are applying an explicit (for some subjects at least) lsquolsquoreject repetitionsrsquorsquorule or that the rejection is part of a more general similarity-based mechanism inwhich test strings are compared (implicitly or explicitly) with memories oflearning strings We will return to this debate in the General Discussion andquestion whether it is possible (within the invariant task) to distinguish betweenrule- and similarity-based behaviour

Our finding of further evidence that subjects are not learning the experi-mentersrsquo rules in the 3s task leads us to question whether performance in thelogically related clocks task (Bright amp Burton 1994 1998) is based solely on theexperimentersrsquo rule pertaining to the invariant time range It is possible that theuse of information correlated with the rule that we and others (eg Cock et al1994 Wright amp Burton 1995) have observed in the digit task may be due to thenature of the numeric stimuli used It is plausible that certain structural char-acteristics of the number strings lend themselves to this type of processing Aclearer indication of a generic mechanism underlying invariant learning would

INVARIANT LEARNING 191

come from finding that the observed effects generalise to the more complexclock stimuli of Bright and Burton (1994 1998)

EXPERIMENT 2

A logical way to look for similar effects would be to test for a rejection strategyusing the clock stimuli However the nature of the stimuli make it extremelydifficult to design a lsquolsquorejectionrsquorsquo test set In our minds there seems to be nocorrelated feature (such as repetitions) that varies with the invariant time rangeLikewise manipulation of the specific similarity of learning and test items is alsoproblematic due to the way in which the clock stimuli are constructed For thisreason we manipulated other properties of the test pairs that we hypothesisedwould have an effect on subjectsrsquo decisions at test Bright and Burton (19941998) argued that performance in the clock task was indicative of implicit ruleabstraction If subjects are abstracting a rule during learning then presumably itwould be of the form lsquolsquofavour times between 6 and 12rsquorsquo (Bright amp Burton 1994p 81) If we accept this then provided one time in each pair is between 6 and 12and the other time is outside this range we would expect to observe the normalselection preference Alternatively subjects may be engaging in a comparisonprocess similar to the one that may underlie the rejection strategy If subjects aremaking comparisons of test items with learning items then reducing the similaritybetween learning and test items should be detrimental to performance InExperiment 2 we contrast performance on test pairs with differing degrees ofintra-test pair similarity Test pairs with a low similarity between times (thoseseparated by 6 hours eg 830 vs 230) are compared with pairs with a mediumsimilarity (those separated by 3 hours eg 430 vs 730) and with pairs with ahigh similarity (those separated by 1 hour eg 510 vs 610) If performance isbased on the lsquolsquo6 to 12rsquorsquo rule we expect no differences between the pair typesHowever if subjects are engaged in similarity-based processing we expectselection of the invariant in the 1-hour pairs to be lower than in the 6-hour pairs

Any observed differences between the pair types could be due to subjectsbeing biased into making comparisons by the nature of the pre-test instructionCock et al (1994) raised the possibility that the instruction to rely on memorycues subjects to engage in a post hoc comparison To test this claim they con-ducted a standard 3s task but replaced the memory instruction with a lsquolsquorulersquorsquoinstruction (Cock et al 1994 Experiment 3) Prior to the test phase of theexperiment subjects were informed that all learning items conformed to asimple rule and that test items conforming to this rule should be selectedPatterns of performance were similar to those of normal lsquolsquomemoryrsquorsquo instructionsubjects In Experiment 2 we control for the possibility of instructional bias onpair type selection We directly compare the performance of a group given thestandard memory instruction at test with one given an instruction to classifyitems on the basis of a rule

192 NEWELL AND BRIGHT

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

results in reduced priming effects (eg Blaxton 1989 Jacoby amp Hayman1987)

In Experiment 1 we test the rejection strategy of Wright and Burton (1995)and examine whether subjectsrsquo tendency to reject items containing repeateddigits interacts with a change in the perceptual format of items between thelearning and test phase If an interaction were obtained this would suggest thatthe rejection strategy proposed by Wright and Burton is not a genericmechanism underlying performance in the invariant 3s task An interactionwould suggest that the tendency to reject distinctive items is observed only whenthe perceptual format of learning and test items is the same In contrast thefailure to find an interaction would demonstrate that the rejection strategyoperates under both same and cross-format transfer conditions

EXPERIMENT 1

Method

Participants Thirty undergraduate students from the University of NewSouth Wales participated in the experiment in return for course credit All wereaged between 18 and 30 years All were na otilde Egrave ve with respect to the invariantlearning procedure

Materials Learning sets were generated by selecting randomly 30 numberstrings from a database containing all 2048 possible four-digit numbersconstructed from the digits 1 to 9 and containing a single digit 3 Test setswere generated from four databases one containing all possible four digitnumbers with a single lsquolsquo3rsquorsquo and with no repetitions one with a single lsquolsquo3rsquorsquo andwith repetitions one with no lsquolsquo3rsquorsquo and no repetitions and one with no lsquolsquo3rsquorsquo andwith repetitions Following Wright and Burton (1995) quadruples triples anddouble doubles were removed from the databases leaving only doubles to serveas distinctive items Items containing a 3 were termed positives and thosewithout a 3 negatives Test sets contained three types of pairs those biasingsubjects towards positive selection those biasing subjects against positiveselection and those that were neutral with respect to positive selection That is

(1) the negative contained a double but positive did notmdashthis should biassubjects towards selection of the positive (eg 5772 vs 2367)

(2) the positive contained a double but negative did notmdashthis should biassubjects against selection of the positive (eg 3525 vs 2167)

(3) that neither the positive nor the negative contained a doublemdashthis shouldbe neutral with respect to selection of the positive (eg 3428 vs 7865)

Each subject received twelve pairs four from each of the three pair types Alllearning items were printed in numeric format (1357) test items were printed ineither numeric or word format (one three five seven)

188 NEWELL AND BRIGHT

Design and procedure A mixed design was used The within-subjectsfactor was direction of bias this had three levels towards neutral against Thebetween-subjects factor was test format with two levels same or changedSubjects were randomly assigned to one of the two groups The lsquolsquosamersquorsquo grouplearned and were tested on numeric items the lsquolsquochangedrsquorsquo group learned onnumeric items and were tested on word items The dependent variable was thenumber of positives selected at test

The experiment consisted of three phases learning an unexpected test andpost-test questioning Subjects were shown 30 four-digit numbers containingthe digit 3 and were asked to perform an addition and comparison task oneach number This involved adding together the first two digits and compar-ing the sum with the total of the second two digits After completing thistask learning materials were removed from sight and subjects were presentedwith 12 test pairs in numeric (same group) or word (changed group) formatand were told (falsely) that they had seen one item in each pair before Theleftright position of the positive and negative and the order of presentation ofthe three pair types were counterbalanced Subjects were asked to indicatewhich item they thought they had seen before and to guess if they wereunsure On completion of the test phase a questionnaire was presented to thesubjects (see the Appendix) On completion of the questionnaire subjectswere fully debriefed

Results

The mean number of positives selected was 613 (out of a maximum of 12) SD= 15 A single sample t-test showed that this was not significantly different fromchance performance of 6 [t(29) = 050 p gt 1] A 2 (Test Format samechanged) 6 3 (Direction of Bias towards neutral against) mixed modelanalysis of variance was conducted This revealed a significant main effect ofdirection of bias [F(2 56) = 462 p lt 05] and no significant effect of testformat [F(1 28) = 185 p gt 05] The interaction between test format anddirection of bias was not significant [F(2 56) = 113 p gt 05] The meannumbers of positives selected in each cell of the 2 6 3 design are presented inTable 1

TABLE 1Mean selection of positives (out of four) and standard

deviations by condition (Experiment 1)

Test format Towards Neutral Against

Same (digit) 273 (122) 193 (110) 207 (110)Changed (word) 253 (119) 213 (099) 133 (097)

INVARIANT LEARNING 189

In order to be confident that subjectsrsquo tendency to reject items containingrepeated digits extended to the changed format condition we conducted a one-way (direction of bias) repeated measures ANOVA on the data from this con-dition A significant main effect [F(2 28) = 442 p lt 05] was founddemonstrating that subjects do tend to reject distinctive items when the per-ceptual format is changed between learning and test phases Planned contrastsconducted on combined data from the same and changed format conditionsshowed a significant difference between the towards and against condition[F(1 28) = 918 MSe = 142 p lt 05 (Fc = 648)] Contrasts between towardsand neutral and against and neutral were not significant Mean selection scoreswere then compared against chance performance (2 for each condition) For thetowards condition more positives were selected than would be expected bychance [t(29) = 292 p lt 01] for the neutral and against conditions selectionwas at chance [t(29) = 18 p gt 1 t(29) = 151 p gt 1 respectively]

Following Wright and Burton (1995) the mean selection scores in eachcondition were converted to percentages to determine the proportion ofresponses that could be classified as involving rejections In the towards con-dition items containing doubles were rejected on 65 of occasions In theagainst condition 42 of items containing doubles were selected leaving 58rejected This means that over these two conditions 61 of decisions wereclassified as involving rejection of items containing repeated numbers Thiscompares to the 54 of decisions involving selection of the items containing theinvariant 3

Test of explicit knowledge All subjects (N = 30) reported that some of theirresponses at test were guesses When questioned about the strategy theyemployed when guessing seven could provide no justification for their guessesand a further thirteen mentioned memory or familiarity without elaborating onthe way in which it was used However four subjects reported relatively detailedstrategies including rejecting items with totals that equalled each otherchoosing items with totals closer together (eg 7673 over 2198) and choosingthe item in which the left pair total was larger than the right pair due to aperceived preponderance of these items in the learning set Analysis of thelearning and test sets used by these subjects revealed that performance predictedby the use of these strategies approximately matched actual performance in allcases This finding indicates that these subjects were using explicit veridicalknowledge and not merely providing post hoc explanations of their behaviour Afurther six subjects mentioned grounding their responses on double digits (bydouble they referred only to contiguous doubles eg 77 or seven seven) Thesesubjectsrsquo responses were further analysed to see if they conformed to theirexplicit knowledge We found that when the contiguous double was in thenegative item (towards condition) positives were selected on 83 of occasionsin comparison when the contiguous double was in the positive item (against

190 NEWELL AND BRIGHT

condition) selection of the positive was at 33 This suggests that these subjectswere responding to some extent on the basis of the presence or absence ofdouble digits In terms of positive selection these subjects did not appear toperform any better than subjects who did not rely on explicit knowledge ofdouble digits 66 (SD 149) compared to 55 (SD 164) Neither groupperformed significantly differently from chance (ps gt 1)

Finally explicit knowledge of the invariant 3 was examined When asked tocircle the number that they thought had appeared most frequently in the learningitems eight subjects circled the number 3 This is more than the 33 subjectspredicted by chance The mean positive selection for these subjects was 60(chance performance) and marginally lower than the mean for the whole group(613) This finding suggests that knowledge of the 3 was not used in the testphase but may have been cued by the questionnaire Many subjects expressedsurprise when told about the nature of the experiment during debriefing

Discussion

Experiment 1 has demonstrated that subjectsrsquo tendency to reject items con-taining repeated digits does not interact with a change in the perceptual formatbetween learning and test items Prior to Experiment 1 the rejection strategy hadnot been tested in cross-format transfer conditions leaving open the possibilitythat the effects observed by Wright and Burton were due to perceptual-basedrecognition We can now be confident that the rejection strategy can account forboth same-format and cross-format versions of the invariant digit task

Experiment 1 has provided further stronger evidence that subjects in theinvariant digit task do not learn the rule that it was originally supposed subjectslearnt in this task (ie lsquolsquoSelect items containing a 3rsquorsquo) The question of whatknowledge subjects are acquiring remains open to debate It is possible thatsubjects are applying an explicit (for some subjects at least) lsquolsquoreject repetitionsrsquorsquorule or that the rejection is part of a more general similarity-based mechanism inwhich test strings are compared (implicitly or explicitly) with memories oflearning strings We will return to this debate in the General Discussion andquestion whether it is possible (within the invariant task) to distinguish betweenrule- and similarity-based behaviour

Our finding of further evidence that subjects are not learning the experi-mentersrsquo rules in the 3s task leads us to question whether performance in thelogically related clocks task (Bright amp Burton 1994 1998) is based solely on theexperimentersrsquo rule pertaining to the invariant time range It is possible that theuse of information correlated with the rule that we and others (eg Cock et al1994 Wright amp Burton 1995) have observed in the digit task may be due to thenature of the numeric stimuli used It is plausible that certain structural char-acteristics of the number strings lend themselves to this type of processing Aclearer indication of a generic mechanism underlying invariant learning would

INVARIANT LEARNING 191

come from finding that the observed effects generalise to the more complexclock stimuli of Bright and Burton (1994 1998)

EXPERIMENT 2

A logical way to look for similar effects would be to test for a rejection strategyusing the clock stimuli However the nature of the stimuli make it extremelydifficult to design a lsquolsquorejectionrsquorsquo test set In our minds there seems to be nocorrelated feature (such as repetitions) that varies with the invariant time rangeLikewise manipulation of the specific similarity of learning and test items is alsoproblematic due to the way in which the clock stimuli are constructed For thisreason we manipulated other properties of the test pairs that we hypothesisedwould have an effect on subjectsrsquo decisions at test Bright and Burton (19941998) argued that performance in the clock task was indicative of implicit ruleabstraction If subjects are abstracting a rule during learning then presumably itwould be of the form lsquolsquofavour times between 6 and 12rsquorsquo (Bright amp Burton 1994p 81) If we accept this then provided one time in each pair is between 6 and 12and the other time is outside this range we would expect to observe the normalselection preference Alternatively subjects may be engaging in a comparisonprocess similar to the one that may underlie the rejection strategy If subjects aremaking comparisons of test items with learning items then reducing the similaritybetween learning and test items should be detrimental to performance InExperiment 2 we contrast performance on test pairs with differing degrees ofintra-test pair similarity Test pairs with a low similarity between times (thoseseparated by 6 hours eg 830 vs 230) are compared with pairs with a mediumsimilarity (those separated by 3 hours eg 430 vs 730) and with pairs with ahigh similarity (those separated by 1 hour eg 510 vs 610) If performance isbased on the lsquolsquo6 to 12rsquorsquo rule we expect no differences between the pair typesHowever if subjects are engaged in similarity-based processing we expectselection of the invariant in the 1-hour pairs to be lower than in the 6-hour pairs

Any observed differences between the pair types could be due to subjectsbeing biased into making comparisons by the nature of the pre-test instructionCock et al (1994) raised the possibility that the instruction to rely on memorycues subjects to engage in a post hoc comparison To test this claim they con-ducted a standard 3s task but replaced the memory instruction with a lsquolsquorulersquorsquoinstruction (Cock et al 1994 Experiment 3) Prior to the test phase of theexperiment subjects were informed that all learning items conformed to asimple rule and that test items conforming to this rule should be selectedPatterns of performance were similar to those of normal lsquolsquomemoryrsquorsquo instructionsubjects In Experiment 2 we control for the possibility of instructional bias onpair type selection We directly compare the performance of a group given thestandard memory instruction at test with one given an instruction to classifyitems on the basis of a rule

192 NEWELL AND BRIGHT

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

Design and procedure A mixed design was used The within-subjectsfactor was direction of bias this had three levels towards neutral against Thebetween-subjects factor was test format with two levels same or changedSubjects were randomly assigned to one of the two groups The lsquolsquosamersquorsquo grouplearned and were tested on numeric items the lsquolsquochangedrsquorsquo group learned onnumeric items and were tested on word items The dependent variable was thenumber of positives selected at test

The experiment consisted of three phases learning an unexpected test andpost-test questioning Subjects were shown 30 four-digit numbers containingthe digit 3 and were asked to perform an addition and comparison task oneach number This involved adding together the first two digits and compar-ing the sum with the total of the second two digits After completing thistask learning materials were removed from sight and subjects were presentedwith 12 test pairs in numeric (same group) or word (changed group) formatand were told (falsely) that they had seen one item in each pair before Theleftright position of the positive and negative and the order of presentation ofthe three pair types were counterbalanced Subjects were asked to indicatewhich item they thought they had seen before and to guess if they wereunsure On completion of the test phase a questionnaire was presented to thesubjects (see the Appendix) On completion of the questionnaire subjectswere fully debriefed

Results

The mean number of positives selected was 613 (out of a maximum of 12) SD= 15 A single sample t-test showed that this was not significantly different fromchance performance of 6 [t(29) = 050 p gt 1] A 2 (Test Format samechanged) 6 3 (Direction of Bias towards neutral against) mixed modelanalysis of variance was conducted This revealed a significant main effect ofdirection of bias [F(2 56) = 462 p lt 05] and no significant effect of testformat [F(1 28) = 185 p gt 05] The interaction between test format anddirection of bias was not significant [F(2 56) = 113 p gt 05] The meannumbers of positives selected in each cell of the 2 6 3 design are presented inTable 1

TABLE 1Mean selection of positives (out of four) and standard

deviations by condition (Experiment 1)

Test format Towards Neutral Against

Same (digit) 273 (122) 193 (110) 207 (110)Changed (word) 253 (119) 213 (099) 133 (097)

INVARIANT LEARNING 189

In order to be confident that subjectsrsquo tendency to reject items containingrepeated digits extended to the changed format condition we conducted a one-way (direction of bias) repeated measures ANOVA on the data from this con-dition A significant main effect [F(2 28) = 442 p lt 05] was founddemonstrating that subjects do tend to reject distinctive items when the per-ceptual format is changed between learning and test phases Planned contrastsconducted on combined data from the same and changed format conditionsshowed a significant difference between the towards and against condition[F(1 28) = 918 MSe = 142 p lt 05 (Fc = 648)] Contrasts between towardsand neutral and against and neutral were not significant Mean selection scoreswere then compared against chance performance (2 for each condition) For thetowards condition more positives were selected than would be expected bychance [t(29) = 292 p lt 01] for the neutral and against conditions selectionwas at chance [t(29) = 18 p gt 1 t(29) = 151 p gt 1 respectively]

Following Wright and Burton (1995) the mean selection scores in eachcondition were converted to percentages to determine the proportion ofresponses that could be classified as involving rejections In the towards con-dition items containing doubles were rejected on 65 of occasions In theagainst condition 42 of items containing doubles were selected leaving 58rejected This means that over these two conditions 61 of decisions wereclassified as involving rejection of items containing repeated numbers Thiscompares to the 54 of decisions involving selection of the items containing theinvariant 3

Test of explicit knowledge All subjects (N = 30) reported that some of theirresponses at test were guesses When questioned about the strategy theyemployed when guessing seven could provide no justification for their guessesand a further thirteen mentioned memory or familiarity without elaborating onthe way in which it was used However four subjects reported relatively detailedstrategies including rejecting items with totals that equalled each otherchoosing items with totals closer together (eg 7673 over 2198) and choosingthe item in which the left pair total was larger than the right pair due to aperceived preponderance of these items in the learning set Analysis of thelearning and test sets used by these subjects revealed that performance predictedby the use of these strategies approximately matched actual performance in allcases This finding indicates that these subjects were using explicit veridicalknowledge and not merely providing post hoc explanations of their behaviour Afurther six subjects mentioned grounding their responses on double digits (bydouble they referred only to contiguous doubles eg 77 or seven seven) Thesesubjectsrsquo responses were further analysed to see if they conformed to theirexplicit knowledge We found that when the contiguous double was in thenegative item (towards condition) positives were selected on 83 of occasionsin comparison when the contiguous double was in the positive item (against

190 NEWELL AND BRIGHT

condition) selection of the positive was at 33 This suggests that these subjectswere responding to some extent on the basis of the presence or absence ofdouble digits In terms of positive selection these subjects did not appear toperform any better than subjects who did not rely on explicit knowledge ofdouble digits 66 (SD 149) compared to 55 (SD 164) Neither groupperformed significantly differently from chance (ps gt 1)

Finally explicit knowledge of the invariant 3 was examined When asked tocircle the number that they thought had appeared most frequently in the learningitems eight subjects circled the number 3 This is more than the 33 subjectspredicted by chance The mean positive selection for these subjects was 60(chance performance) and marginally lower than the mean for the whole group(613) This finding suggests that knowledge of the 3 was not used in the testphase but may have been cued by the questionnaire Many subjects expressedsurprise when told about the nature of the experiment during debriefing

Discussion

Experiment 1 has demonstrated that subjectsrsquo tendency to reject items con-taining repeated digits does not interact with a change in the perceptual formatbetween learning and test items Prior to Experiment 1 the rejection strategy hadnot been tested in cross-format transfer conditions leaving open the possibilitythat the effects observed by Wright and Burton were due to perceptual-basedrecognition We can now be confident that the rejection strategy can account forboth same-format and cross-format versions of the invariant digit task

Experiment 1 has provided further stronger evidence that subjects in theinvariant digit task do not learn the rule that it was originally supposed subjectslearnt in this task (ie lsquolsquoSelect items containing a 3rsquorsquo) The question of whatknowledge subjects are acquiring remains open to debate It is possible thatsubjects are applying an explicit (for some subjects at least) lsquolsquoreject repetitionsrsquorsquorule or that the rejection is part of a more general similarity-based mechanism inwhich test strings are compared (implicitly or explicitly) with memories oflearning strings We will return to this debate in the General Discussion andquestion whether it is possible (within the invariant task) to distinguish betweenrule- and similarity-based behaviour

Our finding of further evidence that subjects are not learning the experi-mentersrsquo rules in the 3s task leads us to question whether performance in thelogically related clocks task (Bright amp Burton 1994 1998) is based solely on theexperimentersrsquo rule pertaining to the invariant time range It is possible that theuse of information correlated with the rule that we and others (eg Cock et al1994 Wright amp Burton 1995) have observed in the digit task may be due to thenature of the numeric stimuli used It is plausible that certain structural char-acteristics of the number strings lend themselves to this type of processing Aclearer indication of a generic mechanism underlying invariant learning would

INVARIANT LEARNING 191

come from finding that the observed effects generalise to the more complexclock stimuli of Bright and Burton (1994 1998)

EXPERIMENT 2

A logical way to look for similar effects would be to test for a rejection strategyusing the clock stimuli However the nature of the stimuli make it extremelydifficult to design a lsquolsquorejectionrsquorsquo test set In our minds there seems to be nocorrelated feature (such as repetitions) that varies with the invariant time rangeLikewise manipulation of the specific similarity of learning and test items is alsoproblematic due to the way in which the clock stimuli are constructed For thisreason we manipulated other properties of the test pairs that we hypothesisedwould have an effect on subjectsrsquo decisions at test Bright and Burton (19941998) argued that performance in the clock task was indicative of implicit ruleabstraction If subjects are abstracting a rule during learning then presumably itwould be of the form lsquolsquofavour times between 6 and 12rsquorsquo (Bright amp Burton 1994p 81) If we accept this then provided one time in each pair is between 6 and 12and the other time is outside this range we would expect to observe the normalselection preference Alternatively subjects may be engaging in a comparisonprocess similar to the one that may underlie the rejection strategy If subjects aremaking comparisons of test items with learning items then reducing the similaritybetween learning and test items should be detrimental to performance InExperiment 2 we contrast performance on test pairs with differing degrees ofintra-test pair similarity Test pairs with a low similarity between times (thoseseparated by 6 hours eg 830 vs 230) are compared with pairs with a mediumsimilarity (those separated by 3 hours eg 430 vs 730) and with pairs with ahigh similarity (those separated by 1 hour eg 510 vs 610) If performance isbased on the lsquolsquo6 to 12rsquorsquo rule we expect no differences between the pair typesHowever if subjects are engaged in similarity-based processing we expectselection of the invariant in the 1-hour pairs to be lower than in the 6-hour pairs

Any observed differences between the pair types could be due to subjectsbeing biased into making comparisons by the nature of the pre-test instructionCock et al (1994) raised the possibility that the instruction to rely on memorycues subjects to engage in a post hoc comparison To test this claim they con-ducted a standard 3s task but replaced the memory instruction with a lsquolsquorulersquorsquoinstruction (Cock et al 1994 Experiment 3) Prior to the test phase of theexperiment subjects were informed that all learning items conformed to asimple rule and that test items conforming to this rule should be selectedPatterns of performance were similar to those of normal lsquolsquomemoryrsquorsquo instructionsubjects In Experiment 2 we control for the possibility of instructional bias onpair type selection We directly compare the performance of a group given thestandard memory instruction at test with one given an instruction to classifyitems on the basis of a rule

192 NEWELL AND BRIGHT

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

In order to be confident that subjectsrsquo tendency to reject items containingrepeated digits extended to the changed format condition we conducted a one-way (direction of bias) repeated measures ANOVA on the data from this con-dition A significant main effect [F(2 28) = 442 p lt 05] was founddemonstrating that subjects do tend to reject distinctive items when the per-ceptual format is changed between learning and test phases Planned contrastsconducted on combined data from the same and changed format conditionsshowed a significant difference between the towards and against condition[F(1 28) = 918 MSe = 142 p lt 05 (Fc = 648)] Contrasts between towardsand neutral and against and neutral were not significant Mean selection scoreswere then compared against chance performance (2 for each condition) For thetowards condition more positives were selected than would be expected bychance [t(29) = 292 p lt 01] for the neutral and against conditions selectionwas at chance [t(29) = 18 p gt 1 t(29) = 151 p gt 1 respectively]

Following Wright and Burton (1995) the mean selection scores in eachcondition were converted to percentages to determine the proportion ofresponses that could be classified as involving rejections In the towards con-dition items containing doubles were rejected on 65 of occasions In theagainst condition 42 of items containing doubles were selected leaving 58rejected This means that over these two conditions 61 of decisions wereclassified as involving rejection of items containing repeated numbers Thiscompares to the 54 of decisions involving selection of the items containing theinvariant 3

Test of explicit knowledge All subjects (N = 30) reported that some of theirresponses at test were guesses When questioned about the strategy theyemployed when guessing seven could provide no justification for their guessesand a further thirteen mentioned memory or familiarity without elaborating onthe way in which it was used However four subjects reported relatively detailedstrategies including rejecting items with totals that equalled each otherchoosing items with totals closer together (eg 7673 over 2198) and choosingthe item in which the left pair total was larger than the right pair due to aperceived preponderance of these items in the learning set Analysis of thelearning and test sets used by these subjects revealed that performance predictedby the use of these strategies approximately matched actual performance in allcases This finding indicates that these subjects were using explicit veridicalknowledge and not merely providing post hoc explanations of their behaviour Afurther six subjects mentioned grounding their responses on double digits (bydouble they referred only to contiguous doubles eg 77 or seven seven) Thesesubjectsrsquo responses were further analysed to see if they conformed to theirexplicit knowledge We found that when the contiguous double was in thenegative item (towards condition) positives were selected on 83 of occasionsin comparison when the contiguous double was in the positive item (against

190 NEWELL AND BRIGHT

condition) selection of the positive was at 33 This suggests that these subjectswere responding to some extent on the basis of the presence or absence ofdouble digits In terms of positive selection these subjects did not appear toperform any better than subjects who did not rely on explicit knowledge ofdouble digits 66 (SD 149) compared to 55 (SD 164) Neither groupperformed significantly differently from chance (ps gt 1)

Finally explicit knowledge of the invariant 3 was examined When asked tocircle the number that they thought had appeared most frequently in the learningitems eight subjects circled the number 3 This is more than the 33 subjectspredicted by chance The mean positive selection for these subjects was 60(chance performance) and marginally lower than the mean for the whole group(613) This finding suggests that knowledge of the 3 was not used in the testphase but may have been cued by the questionnaire Many subjects expressedsurprise when told about the nature of the experiment during debriefing

Discussion

Experiment 1 has demonstrated that subjectsrsquo tendency to reject items con-taining repeated digits does not interact with a change in the perceptual formatbetween learning and test items Prior to Experiment 1 the rejection strategy hadnot been tested in cross-format transfer conditions leaving open the possibilitythat the effects observed by Wright and Burton were due to perceptual-basedrecognition We can now be confident that the rejection strategy can account forboth same-format and cross-format versions of the invariant digit task

Experiment 1 has provided further stronger evidence that subjects in theinvariant digit task do not learn the rule that it was originally supposed subjectslearnt in this task (ie lsquolsquoSelect items containing a 3rsquorsquo) The question of whatknowledge subjects are acquiring remains open to debate It is possible thatsubjects are applying an explicit (for some subjects at least) lsquolsquoreject repetitionsrsquorsquorule or that the rejection is part of a more general similarity-based mechanism inwhich test strings are compared (implicitly or explicitly) with memories oflearning strings We will return to this debate in the General Discussion andquestion whether it is possible (within the invariant task) to distinguish betweenrule- and similarity-based behaviour

Our finding of further evidence that subjects are not learning the experi-mentersrsquo rules in the 3s task leads us to question whether performance in thelogically related clocks task (Bright amp Burton 1994 1998) is based solely on theexperimentersrsquo rule pertaining to the invariant time range It is possible that theuse of information correlated with the rule that we and others (eg Cock et al1994 Wright amp Burton 1995) have observed in the digit task may be due to thenature of the numeric stimuli used It is plausible that certain structural char-acteristics of the number strings lend themselves to this type of processing Aclearer indication of a generic mechanism underlying invariant learning would

INVARIANT LEARNING 191

come from finding that the observed effects generalise to the more complexclock stimuli of Bright and Burton (1994 1998)

EXPERIMENT 2

A logical way to look for similar effects would be to test for a rejection strategyusing the clock stimuli However the nature of the stimuli make it extremelydifficult to design a lsquolsquorejectionrsquorsquo test set In our minds there seems to be nocorrelated feature (such as repetitions) that varies with the invariant time rangeLikewise manipulation of the specific similarity of learning and test items is alsoproblematic due to the way in which the clock stimuli are constructed For thisreason we manipulated other properties of the test pairs that we hypothesisedwould have an effect on subjectsrsquo decisions at test Bright and Burton (19941998) argued that performance in the clock task was indicative of implicit ruleabstraction If subjects are abstracting a rule during learning then presumably itwould be of the form lsquolsquofavour times between 6 and 12rsquorsquo (Bright amp Burton 1994p 81) If we accept this then provided one time in each pair is between 6 and 12and the other time is outside this range we would expect to observe the normalselection preference Alternatively subjects may be engaging in a comparisonprocess similar to the one that may underlie the rejection strategy If subjects aremaking comparisons of test items with learning items then reducing the similaritybetween learning and test items should be detrimental to performance InExperiment 2 we contrast performance on test pairs with differing degrees ofintra-test pair similarity Test pairs with a low similarity between times (thoseseparated by 6 hours eg 830 vs 230) are compared with pairs with a mediumsimilarity (those separated by 3 hours eg 430 vs 730) and with pairs with ahigh similarity (those separated by 1 hour eg 510 vs 610) If performance isbased on the lsquolsquo6 to 12rsquorsquo rule we expect no differences between the pair typesHowever if subjects are engaged in similarity-based processing we expectselection of the invariant in the 1-hour pairs to be lower than in the 6-hour pairs

Any observed differences between the pair types could be due to subjectsbeing biased into making comparisons by the nature of the pre-test instructionCock et al (1994) raised the possibility that the instruction to rely on memorycues subjects to engage in a post hoc comparison To test this claim they con-ducted a standard 3s task but replaced the memory instruction with a lsquolsquorulersquorsquoinstruction (Cock et al 1994 Experiment 3) Prior to the test phase of theexperiment subjects were informed that all learning items conformed to asimple rule and that test items conforming to this rule should be selectedPatterns of performance were similar to those of normal lsquolsquomemoryrsquorsquo instructionsubjects In Experiment 2 we control for the possibility of instructional bias onpair type selection We directly compare the performance of a group given thestandard memory instruction at test with one given an instruction to classifyitems on the basis of a rule

192 NEWELL AND BRIGHT

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

condition) selection of the positive was at 33 This suggests that these subjectswere responding to some extent on the basis of the presence or absence ofdouble digits In terms of positive selection these subjects did not appear toperform any better than subjects who did not rely on explicit knowledge ofdouble digits 66 (SD 149) compared to 55 (SD 164) Neither groupperformed significantly differently from chance (ps gt 1)

Finally explicit knowledge of the invariant 3 was examined When asked tocircle the number that they thought had appeared most frequently in the learningitems eight subjects circled the number 3 This is more than the 33 subjectspredicted by chance The mean positive selection for these subjects was 60(chance performance) and marginally lower than the mean for the whole group(613) This finding suggests that knowledge of the 3 was not used in the testphase but may have been cued by the questionnaire Many subjects expressedsurprise when told about the nature of the experiment during debriefing

Discussion

Experiment 1 has demonstrated that subjectsrsquo tendency to reject items con-taining repeated digits does not interact with a change in the perceptual formatbetween learning and test items Prior to Experiment 1 the rejection strategy hadnot been tested in cross-format transfer conditions leaving open the possibilitythat the effects observed by Wright and Burton were due to perceptual-basedrecognition We can now be confident that the rejection strategy can account forboth same-format and cross-format versions of the invariant digit task

Experiment 1 has provided further stronger evidence that subjects in theinvariant digit task do not learn the rule that it was originally supposed subjectslearnt in this task (ie lsquolsquoSelect items containing a 3rsquorsquo) The question of whatknowledge subjects are acquiring remains open to debate It is possible thatsubjects are applying an explicit (for some subjects at least) lsquolsquoreject repetitionsrsquorsquorule or that the rejection is part of a more general similarity-based mechanism inwhich test strings are compared (implicitly or explicitly) with memories oflearning strings We will return to this debate in the General Discussion andquestion whether it is possible (within the invariant task) to distinguish betweenrule- and similarity-based behaviour

Our finding of further evidence that subjects are not learning the experi-mentersrsquo rules in the 3s task leads us to question whether performance in thelogically related clocks task (Bright amp Burton 1994 1998) is based solely on theexperimentersrsquo rule pertaining to the invariant time range It is possible that theuse of information correlated with the rule that we and others (eg Cock et al1994 Wright amp Burton 1995) have observed in the digit task may be due to thenature of the numeric stimuli used It is plausible that certain structural char-acteristics of the number strings lend themselves to this type of processing Aclearer indication of a generic mechanism underlying invariant learning would

INVARIANT LEARNING 191

come from finding that the observed effects generalise to the more complexclock stimuli of Bright and Burton (1994 1998)

EXPERIMENT 2

A logical way to look for similar effects would be to test for a rejection strategyusing the clock stimuli However the nature of the stimuli make it extremelydifficult to design a lsquolsquorejectionrsquorsquo test set In our minds there seems to be nocorrelated feature (such as repetitions) that varies with the invariant time rangeLikewise manipulation of the specific similarity of learning and test items is alsoproblematic due to the way in which the clock stimuli are constructed For thisreason we manipulated other properties of the test pairs that we hypothesisedwould have an effect on subjectsrsquo decisions at test Bright and Burton (19941998) argued that performance in the clock task was indicative of implicit ruleabstraction If subjects are abstracting a rule during learning then presumably itwould be of the form lsquolsquofavour times between 6 and 12rsquorsquo (Bright amp Burton 1994p 81) If we accept this then provided one time in each pair is between 6 and 12and the other time is outside this range we would expect to observe the normalselection preference Alternatively subjects may be engaging in a comparisonprocess similar to the one that may underlie the rejection strategy If subjects aremaking comparisons of test items with learning items then reducing the similaritybetween learning and test items should be detrimental to performance InExperiment 2 we contrast performance on test pairs with differing degrees ofintra-test pair similarity Test pairs with a low similarity between times (thoseseparated by 6 hours eg 830 vs 230) are compared with pairs with a mediumsimilarity (those separated by 3 hours eg 430 vs 730) and with pairs with ahigh similarity (those separated by 1 hour eg 510 vs 610) If performance isbased on the lsquolsquo6 to 12rsquorsquo rule we expect no differences between the pair typesHowever if subjects are engaged in similarity-based processing we expectselection of the invariant in the 1-hour pairs to be lower than in the 6-hour pairs

Any observed differences between the pair types could be due to subjectsbeing biased into making comparisons by the nature of the pre-test instructionCock et al (1994) raised the possibility that the instruction to rely on memorycues subjects to engage in a post hoc comparison To test this claim they con-ducted a standard 3s task but replaced the memory instruction with a lsquolsquorulersquorsquoinstruction (Cock et al 1994 Experiment 3) Prior to the test phase of theexperiment subjects were informed that all learning items conformed to asimple rule and that test items conforming to this rule should be selectedPatterns of performance were similar to those of normal lsquolsquomemoryrsquorsquo instructionsubjects In Experiment 2 we control for the possibility of instructional bias onpair type selection We directly compare the performance of a group given thestandard memory instruction at test with one given an instruction to classifyitems on the basis of a rule

192 NEWELL AND BRIGHT

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

come from finding that the observed effects generalise to the more complexclock stimuli of Bright and Burton (1994 1998)

EXPERIMENT 2

A logical way to look for similar effects would be to test for a rejection strategyusing the clock stimuli However the nature of the stimuli make it extremelydifficult to design a lsquolsquorejectionrsquorsquo test set In our minds there seems to be nocorrelated feature (such as repetitions) that varies with the invariant time rangeLikewise manipulation of the specific similarity of learning and test items is alsoproblematic due to the way in which the clock stimuli are constructed For thisreason we manipulated other properties of the test pairs that we hypothesisedwould have an effect on subjectsrsquo decisions at test Bright and Burton (19941998) argued that performance in the clock task was indicative of implicit ruleabstraction If subjects are abstracting a rule during learning then presumably itwould be of the form lsquolsquofavour times between 6 and 12rsquorsquo (Bright amp Burton 1994p 81) If we accept this then provided one time in each pair is between 6 and 12and the other time is outside this range we would expect to observe the normalselection preference Alternatively subjects may be engaging in a comparisonprocess similar to the one that may underlie the rejection strategy If subjects aremaking comparisons of test items with learning items then reducing the similaritybetween learning and test items should be detrimental to performance InExperiment 2 we contrast performance on test pairs with differing degrees ofintra-test pair similarity Test pairs with a low similarity between times (thoseseparated by 6 hours eg 830 vs 230) are compared with pairs with a mediumsimilarity (those separated by 3 hours eg 430 vs 730) and with pairs with ahigh similarity (those separated by 1 hour eg 510 vs 610) If performance isbased on the lsquolsquo6 to 12rsquorsquo rule we expect no differences between the pair typesHowever if subjects are engaged in similarity-based processing we expectselection of the invariant in the 1-hour pairs to be lower than in the 6-hour pairs

Any observed differences between the pair types could be due to subjectsbeing biased into making comparisons by the nature of the pre-test instructionCock et al (1994) raised the possibility that the instruction to rely on memorycues subjects to engage in a post hoc comparison To test this claim they con-ducted a standard 3s task but replaced the memory instruction with a lsquolsquorulersquorsquoinstruction (Cock et al 1994 Experiment 3) Prior to the test phase of theexperiment subjects were informed that all learning items conformed to asimple rule and that test items conforming to this rule should be selectedPatterns of performance were similar to those of normal lsquolsquomemoryrsquorsquo instructionsubjects In Experiment 2 we control for the possibility of instructional bias onpair type selection We directly compare the performance of a group given thestandard memory instruction at test with one given an instruction to classifyitems on the basis of a rule

192 NEWELL AND BRIGHT

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

Method

Participants Thirty-two undergraduate students from the University ofNew South Wales participated in the experiment as part of a third-year practicalclass All subjects were aged between 18 and 30 years All were na otilde Egrave ve withrespect to the invariant learning paradigm

Materials Four sets of learning and test items were created Sets 1 and 2used the lsquolsquolatersquorsquo invariant boundary (times between 6 and 12) and sets 3 and4 used the lsquolsquoearlyrsquorsquo invariant (times between 12 and 6) The range of times ineach set spanned the entire allowable interval The basic design of the clockswere similar to those used by Bright and Burton (1994 1998) though somenew designs were added in order to make the induction task more plausibleAll clocks featured either Roman or Arabic numerals Learning itemsconsisted of 30 analogue clock faces printed on four sheets of A4 paper Testitems were pairs of either analogue or digital representations of time Oneitem in each pair was a novel positive (within the invariant boundary) andone was a negative (outside the boundary) The times in each pair wereseparated by 1 hour 3 hours or 6 hours Each test set consisted of 24 pairs intotalmdash8 of each of the test pair types (4 digital and 4 analogue) The leftright position of the invariant and the order of presentation of each test pairtype were counterbalanced Analogue and digital pairs were blocked such thatsubjects either saw 12 analogue pairs followed by 12 digital pairs or viceversa

Design and procedure A mixed design was used There were two within-subjects factors separation with three levels (1 hour 3 hour 6 hour) and testformat with two levels (same changed) The between-subjects factor wasinstruction type with two levels (memory rule) The dependent variable was thenumber of positive items selected at test

Subjects were run together as part of a practical class They were presentedwith the learning items (sets 1ndash4) equally distributed amongst the class and weretold that the study was about clock aesthetics They were asked to look at eachclock in turn and rate it on a five-point scale on how good a representation oftime they thought it depicted Subjects typically took about 5 minutes to com-plete this task On completion of the task learning items were removed andsubjects were given instructions for the test phase Those in the lsquolsquomemoryrsquorsquogroup were told that their memory for the clocks they had rated was to be testedThey were told (falsely) that of the pairs to be presented they had seen one andonly one of the times in each pair before They were asked to choose the timethey thought they had seen before and to guess if they were unsure Subjects inthe rule condition were told that all the clocks they had just rated conformed to asimple rule and that one in each to-be-presented pair conformed to that rule and

INVARIANT LEARNING 193

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

one did not They were told to choose the time that conformed to the rule and toguess if they were unsure

Following the test phase all subjects were given a post-test questionnaireThe questionnaire from Experiment 1 was modified to make it relevant to theclock stimuli (see the Appendix) Once subjects had written answers to all thequestions they were fully debriefed

Results

Two subjects were removed from the analysis as they revealed explicitknowledge pertaining to the invariant and evidence of the use of this knowledgeat test (see below) The mean number of positives selected for the remainingsubjects (N = 30) was 136 (out of a maximum 24) SD = 30 A single sample t-test showed that this was significantly different from chance performance of 12[t(29) = 288 p lt 05]

A 2 (Instruction Type rule memory) 6 2 (Test Format same changed) 6 3(Separation 1 hour 3 hour 6 hour) mixed model analysis of variance revealed amain effect of separation [F(2 56) = 407 p lt 05] but no main effect of testformat [F(1 28) = 173 p gt 05] or instruction type [F(1 28) = 06 p gt 05]No interactions reached significance Mean selection of positives collapsedacross the instruction type variable are shown in Table 2 Subsequent analyseswere performed on the data collapsed across both the instruction type and testformat variables Planned contrasts revealed a significant difference between the1-hour and 6-hour pairs [F(1 28) = 853 MSe = 176 p lt 05 (Fc = 646)]Contrasts between 6- and 3- and 1- and 3-hour pairs were not significantPositive selection in the three pair types was compared to chance performance(four in each condition) Selection was significantly different from chance in the6-hour pairs [t(29) = 407 p lt 001] In the 3-hour and 1-hour pairs it was not 3hour [t(29) = 108 p gt 10] 1 hour [t(29) = 048 p gt 10]

Test of explicit knowledge Out of 32 subjects tested 7 (3 from the rulegroup and 4 from the memory group) were able to identify accurately theinvariant range of times but out of this 7 only 2 indicated using the knowledge ofthe range at test This was reflected in their scoresmdash24 out of a possible 24

TABLE 2Mean selection of positives (out of four) and standard

deviations by condition (Experiment 2)

Test format 1 hour 3 hour 6 hour

Same (analogue) 203 (125) 183 (121) 263 (116)Changed (digital) 210 (092) 250 (090) 253 (090)

194 NEWELL AND BRIGHT

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

selections of the positive These two subjects were excluded from the mainanalysis The mean positive selection of the remaining five subjects was 156(compared to the overall mean of 136) suggesting that they were usingknowledge of the range even though they claimed to be guessing when askedhow they were making their decisions (question 4) In terms of strategies usedsome simply reported guessing or relying on instinct and lsquolsquogut feelingrsquorsquo whereasothers mentioned using familiarity or memory In total 69 of subjects in thememory group reported using familiarity compared with only 31 in the rulegroup No subject reported the correct rule in response to the question that askeddirectly what the rule might be

Discussion

Experiment 2 has demonstrated that the more similar test times are (in terms ofhours) the fewer the positives selected at test We suggested that if subjects wereacquiring the 6 to 12 rule then provided times fell on either side of the invariantboundary selection patterns should be unaffected by the similarity of test pairsThe failure to find this pattern of results demonstrates that subjects have notlearnt the experimentersrsquo rule pertaining to the lsquolsquo6 to 12rsquorsquo time range

This finding indicates that it is not only the invariant digit task that is open toreinterpretation performance in the clock task too can be accounted for by thelearning of correlated information However as with the digit task the nature ofthis information is not immediately apparent It is plausible that subjects arelearning a less well-defined or fuzzy rule (eg lsquolsquoSelect later timesrsquorsquo) that is onlysufficient to produce above chance performance when test times are separatedby a 6-hour margin Equally subjects could be engaging in a similarity matchingprocess that can operate when test times are dissimilar but breaks down when thesimilarity between times is increased We will return to these explanations inmore detail in the General Discussion

The nature of instructions given to subjects before the test phase did not affectperformance This is consistent with Cock et al (1994 Experiment 3) who foundusing the digit task that selection was unaffected by the instruction to classify onthe basis of a rule Further consistencies between this experiment and Cock et al(1994) were found in the analysis of verbal reports In both experiments a lowerpercentage of subjects instructed to use a rule mentioned relying on familiaritywhen making test decisions This indicates that though performance is unaffectedby instructions verbal reports do seem to be influenced by them

The extended questionnaire revealed a degree of relevant explicit knowledgeHowever it was difficult to distinguish between knowledge that was explicit andused at test from knowledge cued by the questionnaire It is plausible thatsubjects make their selections at test believing that they are guessing and thenwhen prompted to think about the range of times seen on the learning items areable to come up with the correct answer

INVARIANT LEARNING 195

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

These problems in interpreting data from post-test questionnaires are echoedin many reviews of the implicit learning literature (eg Shanks amp St John1994) in which questionnaires are criticised for being too insensitive a measureof task relevant knowledge Although as Wright and Burton (1995) argue therelative simplicity of the materials and the shortness of the test phase in theinvariant task makes it more suited than most to these lsquolsquoinsensitiversquorsquo tests ofexplicit knowledge it is still difficult to assess subjectsrsquo awareness of theknowledge guiding their performance during the test phase For this reason inExperiment 3 we adopt a method for measuring explicit knowledge reported byDienes Altmann Kwan and Goode (1995) in the artificial grammar learningliterature Instead of inviting subjects to reflect on the basis of their decisionsafter completing the test we use confidence ratings to record a measure ofparticipantsrsquo subjective confidence in each decision during the test phase Thison-line measure circumvents the problem of cuing explicit knowledge with post-test questions thus allowing us to draw a firmer conclusion about the implicit orexplicit status of the acquired knowledge

Dienes (Dienes et al 1995 Dienes amp Berry 1997) has suggested that oneway in which knowledge may be implicit is in the sense that subjects do notknow that they have it In other words they lack metaknowledge about theirknowledge (Dienes amp Altmann 1997 Dienes et al 1995 Shanks amp Johnstone1998) If subjects in the invariant task do lack metaknowledge then we can maketwo predictions First subjects should be no more confident in correct decisionsthan in incorrect decisions (Dienes et al 1995) Second subjects should stilldemonstrate above-chance performance even when they claim to be literallyguessing (Cheesman amp Merikle 1986 Dienes et al 1995) On the other hand ifperformance is mediated by potentially explicit knowledge we expect theopposite pattern of results higher confidence in correct than incorrect decisionsand guess responses associated with chance performance

EXPERIMENT 3

Experiment 3 followed the same procedure as the memory group fromExperiment 2 However at test subjects were required to rate their confidencein each selection decision on a five-point scale Performance of subjects giventhe usual incidental instructions prior to learning was compared with that ofsubjects instructed to try and work out the invariant time range This secondgroup was included so that we could be more confident in drawing conclusionsabout the knowledge used by subjects in the task (Berry amp Cock 1998)

Method

Participants Twenty-eight undergraduate students from the University ofNew South Wales participated in the experiment in return for course credit Allsubjects were aged between 18 and 30 years None had taken part in previousinvariant learning experiments

196 NEWELL AND BRIGHT

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

Materials In Experiment 2 no differences were found between lsquolsquoearlyrsquorsquo andlsquolsquolatersquorsquo invariant times so only late (6 to 12) times were used in Experiment 2 Inaddition no differences were found between analogue and digital format testpairs so in this experiment only digital format test pairs were used Two new lsquolsquo6to 12rsquorsquo invariant sets were created with corresponding test sets Test setsconsisted of 12 pairsmdash4 each of the 1- 3- and 6-hour types Learning items wereprinted on A4 paper with a rating scale under each clock To aid with datacollection test pairs were presented on a computer monitor Confidence ratingscales were printed on a separate piece of papermdash1 indicated lsquolsquocomplete guessrsquorsquoand 5 lsquolsquocomplete certaintyrsquorsquo

Design and procedure This was a single-factor within-subjects design Thefactor was separation with three levels 1 hour 3 hour and 6 hour The dependentvariable was number of positives selected at test Subjects were given the learningitems and asked to rate each clock on how good a representation of time it showedby marking the appropriate phrase on the scale On completion of this tasksubjects sat in front of a monitor and were told to choose the time they thoughtthey had seen previously from the to-be-presented pairs Subjects satapproximately 40 cm from the screen they made selections by pressing labelledlsquolsquoLrsquorsquo and lsquolsquoRrsquorsquo keys that corresponded to the time on the left or right of the pairAfter making each response subjects were instructed to circle a number from 1 to5 on the confidence-rating scale In addition to the 28 subjects given the standardincidental instruction a further 12 subjects (taken from the same subject pool)were given the following explicit instruction prior to the learning phase

Please look carefully at all the clocks on the sheets of paper in front of you All thetimes shown on the clocks fall within a particular range of hours (ie betweenX00 and Y00) Please try to work out the range of hours shown on the clocks asthis information will help you in a subsequent test

Once subjects had completed the test phase both groups were given the samequestionnaire as used in Experiment 2 with the addition of one question Theadded question read as follows

(7) Did you use your knowledge of the time range to help you make your decisionsduring the test or did you just think of it when answering question 6

This was included in an attempt to distinguish between knowledge used at testand knowledge cued by post-test questions

Results and discussion

Subjects in the group that did not receive instructions about the invariant rangeprior to learning are termed lsquolsquoincidentalrsquorsquo those in the group that did are termedlsquolsquoexplicitrsquorsquo The mean number of positives selected for the incidental group was

INVARIANT LEARNING 197

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

764 (out of a maximum of 12) SD = 164 A single sample t-test showed thatthis was significantly different from chance [t(27) = 531 p lt 001] For theexplicit group 1183 SD = 39 positives were selected This was also sig-nificantly different from chance [t(11) = 5191 p lt 001] A single factorrepeated measures analysis of variance on the incidental group scores revealedno effect of separation [F(2 54) = 160 p lt 1] Similarly no effect was foundfor the explicit group Mean positive selection in the three pair types for theincidental group is shown in Table 3 Positive selection was compared to chanceperformance (two in each condition) This revealed that selection was abovechance for the 6-hour pairs [t(27) = 373 p lt 001] and the 3-hour pairs [t(27)= 373 p lt 001] but not for the 1-hour pairs [t(27) = 161 p gt 1] For theexplicit group selection was above chance for all three pair types

Confidence ratings The minimum confidence rating was 1 and themaximum was 5 Overall mean confidence for the incidental group was 232SD = 78 for the explicit group it was 410 SD = 58 Mean confidence for thethree pair types for the incidental group is shown in Table 4 A 1 6 3 Separation(1 hour 3 hour 6 hour) within-subjects ANOVA on the incidental groupconfidence data revealed a main effect of separation [F(2 54) = 633 p lt 05]Planned contrasts revealed significant differences between confidence on the 1-and 3-hour pairs [F(1 27) = 919 MSe = 24 p lt 05] Contrasts between the 1-and 6-hour pairs were not significant

Confidence in incorrect and correct decisions was averaged for all incidentalsubjects A difference in confidence between correct and incorrect decisions wastaken as a measure of metaknowledge Mean confidence in correct decisionswas 243 SD = 76 and in incorrect it was 217 SD = 86 A paired samples t-test

TABLE 4Mean confidence rating (out of five) and standard deviationfor three test pair conditions (Experiment 3) (incidental group)

Separation 1 hour 3 hour 6 hour

210 (087) 250 (088) 232 (79)

TABLE 3Mean selection of positives (out of four) and standard

deviations (Experiment 3)

Test format 1 hour 3 hour 6 hour

Changed (digital) 229 (090) 264 (090) 271 (100)

198 NEWELL AND BRIGHT

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

showed a significant difference between these means [t(26)1 = 213 p lt 05] Inthe explicit group only three out of twelve subjects made incorrect decisions andthese subjects only made one incorrect decision each For this reason a com-parison of correct and incorrect decisions was not appropriate Mean level ofconfidence in correct decisions was 409 SD = 57 and in incorrect decisions itwas 367 SD = 231

For the incidental group responses given a confidence rating of 1 (completeguess) were analysed to see if performance differed from chance If C representsthe number of Correct responses thought to be a guess and I the number ofIncorrect responses thought to be a guess then CndashI gives us a measure of lowconfidence knowledge (Dienes et al 1995) A score of 0 would indicate randomresponding Mean value of CndashI was 91 SD = 267 a single sample t-testrevealed that this was not significantly different from 0 [t(21)2 = 160 p gt 1]The upper limit of the 95 confidence interval for this difference was 209

Test of explicit knowledge One subject from the incidental group correctlyidentified the range of times but in response to question 7 said that they hadonly thought about it after reading question 6 This subjectrsquos score was 7 andtheir overall confidence was 275 Out of 28 subjects 19 mentioned usingfamiliarity or trying to visualise learning items Many subjects expressedsurprise when told about the invariant time range during debriefing In contrastall 12 subjects in the explicit group correctly identified the range of times andsaid that they had used knowledge of the range to make their decisions at test

The aim of Experiment 3 was to assess the implicit or explicit status of theknowledge underlying performance in the clock task Confidence rating datashowed that incidental subjects were more confident in their correct decisionsthan in their incorrect decisions This suggests that subjects were aware of whenthey were applying knowledge as opposed to merely guessing (Dienes amp Alt-mann 1997) In other words subjects possessed metaknowledge Furthermorefor the decisions in which subjects claimed to be literally guessing (a confidencerating of 1) responses were no different from random responding This randomresponding implies that there is no underlying influence of implicit knowledgeIn order to determine the robustness of this interpretation of the guessingcriterion we examined the sensitivity of the test to pick up the influence ofimplicit knowledge The mean number of guess responses for subjects in theincidental group was 385 (out of a possible 12) The mean invariant selectionfor this group was 76412 thus the maximum expected number of correctresponses is (76412) 6 385 and the maximum expected number of incorrectresponses is (43612) 6 385 Given this the maximum mean expected dif-ference score is (764 7 436) 6 38512 = 328 6 032 = 105 This analysis

1There was missing data for one subject who made no incorrect decisions2Missing data for six subjects who gave no confidence ratings of 1

INVARIANT LEARNING 199

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

demonstrates that the maximum mean expected difference score (105) liesinside the upper limit of the 95 confidence interval (209) reported earlier3 Weare therefore unable on the basis of the guessing criterion to rule out thepresence of implicit knowledge Furthermore we acknowledge that possibleindividual differences in the interpretation of the scale and in willingness toreport low confidence knowledge may have resulted in our measure being arather conservative estimate of implicit knowledge

Post-test questionnaires which revealed minimal verbal knowledge of theinvariant suggest the presence of some implicit knowledge It seems thatalthough some decisions were associated with higher levels of confidence theunderlying knowledge was not fully available to verbal report and thus may havebeen implicit Explicit subjects who were provided with a strategy for successperformed as expected better than incidental subjects (in terms of positiveselection) and exhibited higher levels of confidence and relevant explicitknowledge

The failure to find a main effect of separation in the positive selection data isinconsistent with Experiment 2 This failure is probably due to a loss of powerresulting from the reduction in the number of test pairs from 24 to 12 Supportfor this conclusion comes from the finding of a significant main effect ofseparation across Experiments 2 and 3 [F(2 112) = 391 p lt 05] and a non-significant Separation (1 3 6 hour) 6 Experiment (Experiment 2 Experiment3) interaction [F(2 112) = 111 p gt 1] Mean trends and comparisons to chanceare also consistent with this explanation

Also somewhat counter-intuitive is the finding that subjects were mostconfident in decisions concerning the 3-hour separation pairs One possibleexplanation for this is that some 6-hour pairs contained items in which bothtimes were close to the invariant boundary (eg 650 vs 1250) this may haveconfused some subjects leading to lower levels of confidence In summaryExperiment 3 has provided stronger evidence that performance in the invarianttask is not mediated solely by implicit knowledge

GENERAL DISCUSSION

On first inspection the invariant learning paradigm seems to provide straight-forward evidence for the implicit learning of an abstract rule Reanalysis of theoriginal phenomenon has resulted in a reconsideration of that conclusion Thereis now a growing body of evidence suggesting that performance in the invariantlearning tasks does not rely on subjectsrsquo implicitly acquiring the rules that it wasoriginally assumed were learnt (Churchill amp Gilmore 1998 Cock et al 1994Wright amp Burton 1995) The three experiments presented here contribute to thatbody of evidence We argue that our findings are difficult to reconcile under the

3We thank Referee 2 for suggesting this analysis

200 NEWELL AND BRIGHT

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

original explanations of the invariant digit and clock task In Experiment 1 ifsubjects performed purely on the basis of the invariant 3 rule then the mani-pulation of repeated digits would have had no effect Similarly in Experiment 2performance based on a lsquolsquo6 to 12rsquorsquo rule predicts no difference between theselection of 6-hour and 1-hour pairs Finally processing mediated by implicitknowledge predicts no relationship between confidence and accuracy in deci-sions In all these instances we found significant effects

The representation of knowledge

The finding that subjects are not learning the original experimentersrsquo rule leavesthe issue of what knowledge subjects are acquiring open to question The resultsof Experiment 1 suggest consistent with the findings of Wright and Burton(1995) that subjects learn about the relative distribution of repetitions inlearning and test strings and that this knowledge enables subjects to reject thedistinctive repetition containing strings Wright and Burton tentatively con-cluded that this knowledge was instantiated as an explicit rule We suggest thatthe pattern of rejection equally may be due to subjects making judgements basedon an analogy to learning items It is plausible that over the course of the testphase subjects abstract the lsquolsquoreject repetitionsrsquorsquo rule but in order for thisabstraction to occur the initial stages of the test phase (eg the first three or fourpairs) must involve a process of making similarity matches with memories oflearning strings A subject engaging in such a process will tend to reject theitems containing repetitions as they are highly distinctive and thus less similarto the majority of learning items that do not contain repetitions (Wright ampBurton 1995)

We argue that this more general form of similarity matching also provides agood explanation of performance in the clocks task As suggested by Cock et al(1994) it is plausible that because of possible ambiguities in the placing of handson the clock faces subjects may encode times seen in the learning phase in arather approximate fashion Thus when confronted with a 1-hour pair (eg 550vs 650) at test comparison with a partial memory for a learning time lsquolsquoaround 5or 6rsquorsquo would result in the inability to discriminate the positive (650) from thenegative (550) time In contrast a subject presented with a 6-hour pair (eg825 vs 225) may have a partial memory for a time lsquolsquoaround 830rsquorsquo and inaddition have the feeling that times around 2 were not seen Thus subjects mayeither accept the positive time actively on the basis of its similarity to partialmemories of learning items or passively through the rejection of an item that isdissimilar to any previously encountered times The removal of the dissimilartime in the 1-hour pairs renders this comparison process ineffective and thusresults in the inability to perform the task successfully Subjectsrsquo verbal reportsthat include statements of the form lsquolsquoI know I did not see time Xrsquorsquo support thisexplanation (see Churchill amp Gilmore 1998 for a similar argument)

INVARIANT LEARNING 201

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

In summary we are not able to distinguish equivocally between rule-based andsimilarity-based processing but at the very least we argue that the initial stages ofthe test phase must involve some similarity matching However it is possible thatover the course of the test phase a lsquolsquoreject repetitionsrsquorsquo or a fuzzy lsquolsquoselect latertimesrsquorsquo rule may be abstracted It is perhaps therefore safest to conclude that theinvariant tasks are most likely to involve a combination of rule-based andsimilarity-based processing This conclusion is consistent with computationalmodels of other implicit learning paradigms eg sequence learning (Cleeremans1994) findings from artificial grammar learning tasks (Vokey amp Brooks 1994)and studies of category learning (Nosofsky Clark amp Shin 1989) that all provideevidence for both rule and similarity-based processing

Finally the cross-format transfer effects found in the three experimentsindicate that the underlying representation of knowledge includes more thansimple surface feature information However in itself this finding does notenable us to distinguish between rule- and similarity-based processing becauseevidence for abstract representations is equally consistent with both forms ofprocessing (Hahn amp Chater 1998)

Implicit and explicit knowledge

We argued that the finding that subjects were more confident on trials in whichthey were correct than on those in which they were incorrect indicated thepresence of some metaknowledge Furthermore analysis of subjectsrsquo guessingresponses failed to reveal any influence of implicit knowledge To conclude fromthese findings that invariant learning is based exclusively on explicit knowledgewould be over-interpreting our data The discrepancy between subjectsrsquo verba-lisable knowledge and their confidence the overall low confidence of incidentalsubjects (in comparison to explicit subjects) and their genuine surprise duringdebriefing all suggest otherwise We acknowledge that we may have been unableto detect implicit knowledge due to a lack of power and because of the difficultiesinherent in dissociating implicit from explicit knowledge Invariant learning aswith many of the tasks used to investigate implicit learning suffers from theproblem that the response focused upon (selection of the positive) is not neutralwith respect to potential contamination by explicit knowledge (Vinter amp Per-ruchet 1999) Performance based on implicit knowledge results in the sameoutcomemdashabove-chance selection of the positivemdashas performance based onexplicit knowledge of the invariant characteristic (or correlated information)Consequently dissociating the influence of implicit and explicit knowledge onperformance is problematic (see Jacoby 1991 Jacoby Toth amp Yonelinas 1993)This difficult issue is beginning to be addressed in the literature through thedevelopment of new experimental tasks For example Vinter and Perruchet(1999) reported an innovative drawing task in which they were able todemonstrate the influence of implicit processes because the observed adaptations

202 NEWELL AND BRIGHT

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

in drawing practice could not be expected by conscious exploitation of explicitknowledge Though our results do not deny the existence of implicit knowledgewe can conclude (from our finding of metaknowledge) that contrary to earlierinterpretations (eg McGeorge amp Burton 1990 Bright amp Burton 1994)invariant learning is not mediated purely by implicit knowledge

In summary we believe that our data are most consistent with the view thatsubjects acquire a mixture of implicit and explicit knowledge (see Dienes ampBerry 1997) This view is echoed by the findings of Dienes et al (1995) whoreport that in an artificial grammar learning task subjects in three experimentsexhibited both implicit knowledge evidenced by above-chance performancewhen claiming to be guessing and explicit knowledge through greater con-fidence in correct decisions Shanks and Johnstone (1998 1999) report similarfindings using the sequence learning task though in sequence learning theevidence for implicit knowledge appears to be much weaker

Conclusions

The experiments reported here reflect a shift that can be seen in many recentstudies of implicit learning As noted by Cleeremans Destrebecqz and Boyer(1998) in a review early claims for a sophisticated unconscious mechanismcapable of abstracting and applying rules have been replaced by accountsemphasising the importance of task demands during learning and the congruencebetween learning and test conditions (Whittlesea amp Wright 1997 Wright ampWhittlesea 1998) In accord with this shift in perspective we have presentedfurther stronger evidence against the implicit abstraction of the experimentersrsquorules in the invariant tasks We propose consistent with the learning underlyingmany so-called implicit learning tasks that the invariant tasks involve a mixtureof both implicit and explicit knowledge and a combination of similarity- andrule-based processing Future investigations need to develop more powerfultasks which will allow us to assess the relative contributions of these types ofknowledge and forms of processing to implicit learning

Manuscript received August 1999Revised manuscript received September 2000

REFERENCES

Berry D amp Cock J (1998) Implicit learning of invariant features In MA Stadler amp PA Frensch(Eds) Handbook of implicit learning (pp 135ndash159) Thousand Oaks CA Sage

Blaxton TA (1989) Investigating dissociations among memory measures Support for a transfer-appropriate processing framework Journal of Experimental Psychology Learning Memory andCognition 15 657ndash668

Bright JEH amp Burton AM (1994) Past midnight Semantic processing in an implicit learningtask Quarterly Journal of Experimental Psychology 47A 71ndash89

INVARIANT LEARNING 203

Bright JEH amp Burton AM (1998) Ringing the changes Where abstraction occurs in implicitlearning European Journal of Cognitive Psychology 10 113ndash130

Brooks LR (1978) Non-analytic concept formation and memory for instances In E Rosch amp BLloyd (Eds) Cognition and categorisation Hillsdale NJ Lawrence Erlbaum Associates Inc

Cheesman J amp Merikle PM (1986) Distinguishing conscious from unconscious perceptualprocesses Canadian Journal of Psychology 40 343ndash367

Churchill EF amp Gilmore DJ (1998) Selection through rejection Reconsidering the invariantlearning paradigm Quarterly Journal of Experimental Psychology 51A 1ndash17

Cleeremans A (1994) The representation of structure in sequence prediction tasks In C UmiltaAacute ampM Moscovitch (Eds) Attention and performance XV Conscious and unconscious informationprocessing (pp 783ndash809) Cambridge MA MIT Press

Cleeremans A Destrebecqz A amp Boyer M (1998) Implicit learning News from the frontTrends in Cognitive Sciences 2 406ndash416

Cock JJ Berry DC amp Gaffan EA (1994) New strings for old The role of similarity processingin an incidental learning task Quarterly Journal of Experimental Psychology 47A 1015ndash1034

Dienes Z amp Altmann G (1997) Transfer of implicit knowledge across domains How implicit andhow abstract In DC Berry (Ed) How implicit is implicit learning (pp 107ndash123) Oxford UKOxford University Press

Dienes Z Altmann GTM Kwan L amp Goode A (1995) Unconscious knowledge of artificialgrammars is applied strategically Journal of Experimental Psychology Learning Memory andCognition 21 1322ndash1338

Dienes Z amp Berry D (1997) Implicit learning Below the subjective threshold PsychonomicBulletin and Review 4 3ndash23

Gomez RL (1997) Transfer and complexity in artificial grammar learning Cognitive Psychology33 154ndash207

Gomez RL amp Schvaneveldt RW (1994) What is learned from artificial grammars Transfer testsof simple association Journal of Experimental Psychology Learning Memory and Cognition20 396ndash410

Hahn U amp Chater N (1998) Similarity and rules Distinct exhaustive empirically distinguish-able Cognition 65 197ndash230

Jacoby LL (1991) A process dissociation framework Separating unconscious from intentionaluses of memory Journal of Memory and Language 30 513ndash541

Jacoby LL amp Hayman CA (1987) Specific visual transfer in word identification Journal ofExperimental Psychology Learning Memory and Cognition 13 456ndash463

Jacoby LL Toth JP amp Yonelinas AP (1993) Separating conscious and unconscious influencesof memory Measuring recollection Journal of Experimental Psychology General 122 139ndash154

McGeorge P amp Burton AM (1990) Semantic processing in an incidental learning task QuarterlyJournal of Experimental Psychology 42A 597ndash609

Nosofsky R Clark S amp Shin H (1989) Rules and exemplars in categorization identification andrecognition Journal of Experimental Psychology Learning Memory and Cognition 15 282ndash304

Perruchet P amp Gallego J (1997) A subjective unit formation account of implicit learning In DCBerry (Ed) How implicit is implicit learning (pp 124ndash161) Oxford UK OxfordUniversityPress

Perruchet P amp Pacteau C (1990) Synthetic grammar learning Implicit rule abstraction or explicitfragmentary knowledge Journal of Experimental Psychology General 19 264ndash275

Reber AS (1967) Implicit learning of artificial grammars Journal of Verbal Learning and VerbalBehavior 6 855ndash863

Reber AS (1976) Implicit learning of synthetic languages The role of instructional set Journal ofExperimental Psychology Human Learning and Memory 2 88ndash94

Shanks DR amp Johnstone T (1998) Implicit knowledge in sequential learning tasks In MA Stadleramp PA Frensch (Eds) Handbook of implicit learning (pp 533ndash572) Thousand Oaks CA Sage

204 NEWELL AND BRIGHT

Shanks DR amp Johnstone T (1999) Evaluating the relationship between explicit and implicitknowledge in a sequential reaction time task Journal of Experimental Psychology LearningMemory and Cognition 25 1435ndash1451

Shanks DR amp St John MF (1994) Characteristics of dissociable human learning systemsBehavioral and Brain Sciences 17 367ndash447

Vinter A amp Perruchet P (1999) Isolating unconscious influences The neutral parameter pro-cedure Quarterly Journal of Experimental Psychology 52A 857ndash875

Vokey JR amp Brooks LR (1992) Salience of item knowledge in learning artificial grammarsJournal of Experimental Psychology Learning Memory and Cognition 18 328ndash344

Vokey JR amp Brooks LR (1994) Fragmentary knowledge and the processing-specifi c control ofstructural sensitivity Journal of Experimental Psychology Learning Memory and Cognition20(6) 1504ndash1510

Whittlesea BWA amp Wright RL (1997) Implicit (and explicit) learning Acting adaptivelywithout knowing the consequences Journal of Experimental Psychology Learning Memoryand Cognition 23 181ndash200

Wright RL amp Burton AM (1995) Implicit learning of an invariant Just say no QuarterlyJournal of Experimental Psychology 48A 783ndash796

Wright RL amp Whittlesea BWA (1998) Implicit learning of complex structures Active adaptationand selective processing in acquisition and application Memory and Cognition 26 402ndash420

APPENDIX

Post-test questionnaire used in Experiment 1

(1) Were any of your responses guesses(2) Were you aware of using any strategies when guessing What were the strategies(3) Did you notice anything systematic about the numbers in the first part of the experiment(4) Did any of the numbers appear more frequently than any others(5) One number appeared more frequently than any other during the first part of the experiment

Could you circle the number you think it was If yoursquore not sure please guess

1 2 3 4 5 6 7 8 9

Post-test questionnaire used in Experiments 2 and 3

(1) What do you think the experiment was about(2) Did you notice any peculiarities or common features about the times shown on the clocks that

you rated initially(3) Did you notice any peculiarities or common features about the times presented as pairs in the

second half of the experiment(4) How did you make your decisions when choosing one time from each pair(5) All the times shown on the clocks that you rated initially conformed to a simple rule Have you

any idea what that rule is(6) All the times shown on the clocks that you rated initially fell within a particular time range

Have you any idea what that range is

These questions were printed on the reverse side of the sheet to prevent cueing of knowledgeabout the nature of the invariant

INVARIANT LEARNING 205